I think the key is in the last quoted sentence: there isn't one model. There are many, and they are generated in different ways with differing emphasis on different data sets. They gain confidence when these seem to agree with each other and the acceptable physical knowledge already understood. They also check the sanity of the model to make sure that it is consistent with what has already been observed. In that way anyone may gain confidence that multiple approaches are converging on similar results.

That, and there are metric crap-tonnes of data to work with of all sorts. Just ungodly amounts of it.